A key function for any barter service is to detect circular exchanges in which all demands and supplies of a circle of users are satisfied. We call the demand and supply of a user his queries and data, respectively. The problem of finding a circular exchange is to detect directed cycles in an exchange graph where an edge connects one user's supply to another user's supply that satisfies the first user's demand. Our contributions to solving this problem are two-fold; 1) a process model of constructing an exchange graph, and 2) two cycle detection algorithms that can find all possible directed cycles. Our model processes an incoming user's queries and data across the stored users' data and queries, respectively, by combining database query processing and stream data processing. The algorithms are extensions of depth-first search (DFS) and Strongly-Connected-Component search (SCCS). Experiments show that our enhanced version of SCCS outperforms the enhanced version of DFS by factors ranging from 23 to 132.